01
Substitution
Solve one equation for a variable and substitute it into the remaining equation.
System of Equations Solver
Purpose-built solver page
System of Equations Solver
Use this system of equations solver for two- or three-variable problems, including substitution and elimination. Enter every equation together so the shared solution can be reasoned through step by step.
Type or upload a problemWorked explanationsNo sign-up required
Solve a problem nowsystem of equations solver
{ x + y = 7
Substitution
Elimination
Two or three variables
system of equations solver
Solve your system of equations problem
Enter your system of equations problem below. Add the variable, conditions, and method you want so the AI can return a more relevant worked response.
Text inputImage upload
Step
How to use the System of Equations solver
A complete prompt usually produces a more useful explanation than an isolated expression.
x + y = 11
2x − y = 4
3x = 15
(x, y) = (5, 6)
- 1
Enter every equation
{ x + y = 11Put each equation on its own line and use consistent variable names.
- 2
Choose a method
+ 2x − y = 4Substitution works well when a variable is isolated; elimination works well with matching coefficients.
- 3
Reduce the system
3x = 15Eliminate one variable at a time and show the resulting smaller system.
- 4
Verify the ordered solution
(5, 6) ✓Substitute all values into every original equation.
Tip: ask for a named method, a domain, or a verification step when your course requires one.
system of equations solver
What this System of Equations solver is designed for
The page is organized around the problem types people actually search for, while staying within the text-and-image solver's current capabilities.
02
Elimination
Scale and combine equations so one variable cancels cleanly.
03
Two or three variables
Keep equations aligned and back-substitute in a clear order.
04
Solution classification
Recognize one solution, no solution, or infinitely many solutions from the reduced equations.
Step
Solution classification
Recognize one solution, no solution, or infinitely many solutions from the reduced equations.
(x, y)0 = 10 = 0Example
System of Equations problems to try
These examples reflect common search intent and can be inserted into the solver as a starting point.
Example 1
Solve:
x + y = 11
2x - y = 4A two-variable system suited to elimination.
Example 2
Solve:
y = 3x - 2
2x + y = 18A system where substitution starts naturally.
Example 3
Solve:
x + y + z = 6
2x - y + z = 3
x + 2y - z = 2A three-variable system reduced one variable at a time.
Step
Verify the ordered solution
Substitute all values into every original equation.
x + y = 115 + 6 = 11 ✓
2x − y = 42(5) − 6 = 4 ✓
(x, y)(5, 6) ✓
Formula guides
Understand the formulas used here
Review the related formulas, when to use them, and how they connect in a worked example.
Common mistakes to watch for
A worked answer is most useful when you know which details are easy to lose along the way.
Entering only one equation
A system is defined by all of its equations; missing one changes the problem.
Eliminating inconsistently
When scaling an equation, multiply every term on both sides.
Stopping after one variable
Back-substitute to find the remaining variables and check the full ordered solution.
System of Equations solver FAQ
